Liquid Time-constant Networks

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring the nonlinearity of a learning system by neurons, we impose specialized nonlinearities on the network connections. The obtained models realize dynamical systems with varying (i.e., \emph{liquid}) time-constants coupled to their hidden state, and outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics, and compute their expressive power by the \emph{trajectory length} measure in a latent trajectory representation space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs.